To determine the correct equation for the yearly revenue $R$ of the company $t$ years after a specific year, we need to consider how the revenue changes over time.

Given that the revenue increases by a certain percentage every year, this suggests an exponential growth model. The general form of an exponential growth equation is:

$R = x \cdot (1 + r)^t$

where:

• $x$ is the initial revenue,
• $r$ is the rate of increase (expressed as a decimal),
• $t$ is the number of years after the initial year.

Given the options:

1. $R = x \cdot (0.9)^t$ suggests a decrease by 10% every year (not applicable here since revenue is increasing).
2. $R = x \cdot (1.1)^t$ suggests an increase by 10% every year (this is likely the correct option).
3. $R = x + 0.9t$ suggests a linear increase, not exponential.
4. $R = x + 1.1 \times t$ also suggests a linear increase, not exponential.

Given the information provided, the correct equation representing the yearly revenue $R$ is:

$R = x \cdot (1.1)^t$

This represents a 10% increase in revenue each year.

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Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. How do you calculate the compound annual growth rate (CAGR) from revenue data over several years?
2. How does the exponential growth formula change if the revenue increased by a different percentage?
3. What would the revenue be after 5 years if the initial revenue $x$ was $100,000?
4. How does the choice between linear and exponential models affect revenue predictions?
5. What real-world factors might cause a company's revenue growth to deviate from this model?

Tip: Exponential growth models are commonly used for financial forecasting because they accurately represent consistent percentage increases over time.